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<title>FYL2X—Compute y ∗ log2x </title></head>
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<h1>FYL2X—Compute y ∗ log<sub>2</sub>x</h1>
<table>
<tr>
<th>Opcode</th>
<th>Instruction</th>
<th>64-Bit Mode</th>
<th>Compat/Leg Mode</th>
<th>Description</th></tr>
<tr>
<td>D9 F1</td>
<td>FYL2X</td>
<td>Valid</td>
<td>Valid</td>
<td>Replace ST(1) with (ST(1) ∗ log<sub>2</sub>ST(0)) and pop the register stack.</td></tr></table>
<h2>Description</h2>
<p>Computes (ST(1) ∗ log<sub>2</sub> (ST(0))), stores the result in resister ST(1), and pops the FPU register stack. The source operand in ST(0) must be a non-zero positive number.</p>
<p>The following table shows the results obtained when taking the log of various classes of numbers, assuming that neither overflow nor underflow occurs.</p>
<h3>Table 3-48.  FYL2X Results</h3>
<table>
<tr>
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2"></td>
<th colspan="2">ST(0)</th>
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2"></td></tr>
<tr>
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2">− ∞</td>
<td colspan="2">− F</td>
<td colspan="2">±0</td>
<td colspan="2">+0&lt;+F&lt;+1</td>
<td colspan="2">+ 1</td>
<td colspan="2">+ F &gt; + 1</td>
<td colspan="2">+ ∞</td>
<td colspan="2">NaN</td></tr>
<tr>
<td colspan="2"></td>
<td colspan="2">− ∞</td>
<td colspan="2">*</td>
<td colspan="2">*</td>
<td colspan="2">+ ∞</td>
<td colspan="2">+ ∞</td>
<td colspan="2">*</td>
<td colspan="2">− ∞</td>
<td colspan="2">− ∞</td>
<td colspan="2">NaN</td></tr>
<tr>
<th colspan="2">ST(1)</th>
<td colspan="2">− F</td>
<td colspan="2">*</td>
<td colspan="2">*</td>
<td colspan="2">**</td>
<td colspan="2">+ F</td>
<td colspan="2">− 0</td>
<td colspan="2">− F</td>
<td colspan="2">− ∞</td>
<td colspan="2">NaN</td></tr>
<tr>
<td colspan="2"></td>
<td colspan="2">− 0</td>
<td colspan="2">*</td>
<td colspan="2">*</td>
<td colspan="2">*</td>
<td colspan="2">+ 0</td>
<td colspan="2">− 0</td>
<td colspan="2">− 0</td>
<td colspan="2">*</td>
<td colspan="2">NaN</td></tr>
<tr>
<td colspan="2"></td>
<td colspan="2">+ 0</td>
<td colspan="2">*</td>
<td colspan="2">*</td>
<td colspan="2">*</td>
<td colspan="2">− 0</td>
<td colspan="2">+ 0</td>
<td colspan="2">+ 0</td>
<td colspan="2">*</td>
<td colspan="2">NaN</td></tr>
<tr>
<td colspan="2"></td>
<td colspan="2">+ F</td>
<td colspan="2">*</td>
<td colspan="2">*</td>
<td colspan="2">**</td>
<td colspan="2">− F</td>
<td colspan="2">+ 0</td>
<td colspan="2">+ F</td>
<td colspan="2">+ ∞</td>
<td colspan="2">NaN</td></tr>
<tr>
<td colspan="2"></td>
<td colspan="2">+ ∞</td>
<td colspan="2">*</td>
<td colspan="2">*</td>
<td colspan="2">− ∞</td>
<td colspan="2">− ∞</td>
<td colspan="2">*</td>
<td colspan="2">+ ∞</td>
<td colspan="2">+ ∞</td>
<td colspan="2">NaN</td></tr>
<tr>
<td colspan="2"></td>
<td colspan="2">NaN</td>
<td colspan="2">NaN</td>
<td colspan="2">NaN</td>
<td colspan="2">NaN</td>
<td colspan="2">NaN</td>
<td colspan="2">NaN</td>
<td colspan="2">NaN</td>
<td colspan="2">NaN</td>
<td colspan="2">NaN</td></tr></table>
<p><strong>NOTES:</strong></p>
<p>F Means finite floating-point value.</p>
<p>*</p>
<p>Indicates floating-point invalid-operation (#IA) exception.</p>
<p>** Indicates floating-point zero-divide (#Z) exception.</p>
<p>If the divide-by-zero exception is masked and register ST(0) contains ±0, the instruction returns ∞ with a sign that is the opposite of the sign of the source operand in register ST(1).</p>
<p>The FYL2X instruction is designed with a built-in multiplication to optimize the calculation of logarithms with an arbitrary positive base (b):</p>
<p>log<sub>b</sub>x ← (log<sub>2</sub>b)<sup>–1</sup> ∗ log<sub>2</sub>x</p>
<p>This instruction’s operation is the same in non-64-bit modes and 64-bit mode.</p>
<h2>Operation</h2>
<pre>ST(1) ← ST(1) ∗ log<sub>2</sub>ST(0);
PopRegisterStack;</pre>
<h2>FPU Flags Affected</h2>
<table class="exception-table">
<tr>
<td>C1</td>
<td>
<p>Set to 0 if stack underflow occurred.</p>
<p>Set if result was rounded up; cleared otherwise.</p></td></tr>
<tr>
<td>C0, C2, C3</td>
<td>Undefined.</td></tr></table>
<h2>Floating-Point Exceptions</h2>
<table class="exception-table">
<tr>
<td>#IS</td>
<td>Stack underflow occurred.</td></tr>
<tr>
<td>#IA</td>
<td>
<p>Either operand is an SNaN or unsupported format.</p>
<p>Source operand in register ST(0) is a negative finite value (not -0).</p></td></tr></table>
<p>#Z</p>
<p>Source operand in register ST(0) is ±0.</p>
<p>#D</p>
<p>Source operand is a denormal value.</p>
<p>#U</p>
<p>Result is too small for destination format.</p>
<p>#O</p>
<p>Result is too large for destination format.</p>
<p>#P</p>
<p>Value cannot be represented exactly in destination format.</p>
<h2>Protected Mode Exceptions</h2>
<table class="exception-table">
<tr>
<td>#NM</td>
<td>CR0.EM[bit 2] or CR0.TS[bit 3] = 1.</td></tr>
<tr>
<td>#MF</td>
<td>If there is a pending x87 FPU exception.</td></tr>
<tr>
<td>#UD</td>
<td>If the LOCK prefix is used.</td></tr></table>
<h2>Real-Address Mode Exceptions</h2>
<p>Same exceptions as in protected mode.</p>
<h2>Virtual-8086 Mode Exceptions</h2>
<p>Same exceptions as in protected mode.</p>
<h2>Compatibility Mode Exceptions</h2>
<p>Same exceptions as in protected mode.</p>
<h2>64-Bit Mode Exceptions</h2>
<p>Same exceptions as in protected mode.</p></body></html>